VSEPR theory

Why shape matters

A Lewis structure shows which atoms are joined, but not how they sit in space. Yet shape matters a great deal. Carbon dioxide is straight, and water is bent. That bend makes water polar, and so it dissolves salt and sugar.

The valence shell electron pair repulsion theory, or VSEPR theory, predicts shapes from a simple idea. Sidgwick and Powell proposed it, and Nyholm and Gillespie later improved it.

The ideas of VSEPR

1. The shape depends on the number of electron pairs in the valence shell of the central atom, both bonded and lone.
2. Electron pairs repel each other, because their clouds are negatively charged.
3. The pairs take up positions that keep them as far apart as possible, so the repulsion is least.
4. A double or a triple bond counts as one region, like a single pair. It is a "super pair".
5. Lone pairs are held by one nucleus only, so they spread out more than bonding pairs.

The repulsion falls in this order:

• lone pair with lone pair $>$ lone pair with bond pair $>$ bond pair with bond pair.

Counting the electron pairs

Take the outer electrons of the central atom. Add one for each atom joined by a single bond, such as hydrogen or a halogen. Atoms joined by a double bond, such as oxygen, add nothing. For an ion, add one for each negative charge and take away one for each positive charge.

• $\text{pairs} = \dfrac{V + M \pm q}{2}$, where $V$ is the number of outer electrons of the central atom, $M$ the number of singly bonded atoms and $q$ the size of the charge.
• $\text{lone pairs} = \text{pairs} - \text{bonded atoms}$

For ammonia: nitrogen has $5$ outer electrons and three hydrogens, so there are $\dfrac{5 + 3}{2} = 4$ pairs. Three are bonding pairs, so one is a lone pair.

For sulphur dioxide: sulphur has $6$ outer electrons, and the double-bonded oxygens add none. That gives $\dfrac{6}{2} = 3$ regions: two double bonds and one lone pair.

The five basic shapes

When every pair is a bonding pair, the shape follows straight from the number of pairs.

In a trigonal bipyramid, three pairs lie in a flat triangle round the middle, the equatorial positions. The other two point straight up and down, the axial positions.

Lone pairs change the shape

A lone pair still takes up a corner of the arrangement, but we cannot see it. The shape of a molecule names only the positions of its atoms. And because a lone pair repels more strongly, it pushes the bonding pairs closer together.

Methane, ammonia and water all have four pairs. Watch the angle shrink as lone pairs replace bonding pairs:

• $\text{CH}_4$, no lone pair: $109.5°$.
• $\text{NH}_3$, one lone pair: $107°$.
• $\text{H}_2\text{O}$, two lone pairs: $104.5°$.

Where the lone pairs go

With five pairs, the positions are not all alike. An axial pair has three neighbours at $90°$. An equatorial pair has only two. So a lone pair takes an equatorial position, where it is less crowded. In $\text{SF}_4$ one equatorial lone pair gives the see-saw. In $\text{ClF}_3$ two equatorial lone pairs leave the three fluorines in a T.

With six pairs, all positions are alike. A second lone pair goes opposite the first, as far from it as possible. That is why $\text{XeF}_4$ is square planar.

Practise with new numbers

Try it in Python

The program counts the pairs and lone pairs of six molecules, and looks up each shape in a dictionary.

Common mistakes

• Naming the shape from the pairs. Water has four pairs, a tetrahedral arrangement, but its shape is bent. The shape names the atoms only.
• Counting a double bond as two pairs. A double or triple bond is one region.
• Letting double-bonded oxygen add an electron. Only singly bonded atoms such as hydrogen and the halogens add one each.
• Putting a lone pair in an axial position. With five pairs, lone pairs go equatorial.
• Forgetting the charge of an ion. A negative charge adds electrons, and a positive charge removes them.

Remember these

• Pairs repel and spread out as far as they can. Multiple bonds count as one region.
• Repulsion: lone with lone $>$ lone with bond $>$ bond with bond.
• 2, 3, 4, 5, 6 pairs: linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral.
• Lone pairs squeeze the angles: $109.5°$, $107°$, $104.5°$ for $\text{CH}_4$, $\text{NH}_3$, $\text{H}_2\text{O}$.
• Five pairs: lone pairs equatorial. Six pairs: a second lone pair opposite the first.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. How many electron pairs surround the carbon atom in $\text{CCl}_4$, and what shape is the molecule?

2. Why is the bond angle in ammonia smaller than in methane?

3. What shape is $\text{SF}_4$, and where does its lone pair sit?

4. Carbon dioxide has two double bonds and no lone pair on carbon. What shape does VSEPR give it?

5. Name the shape of a molecule whose central atom has six pairs, two of them lone pairs, and give an example.